Timeline for an identity related to the pentagonal numbers
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14, 2017 at 19:02 | comment | added | Gjergji Zaimi | @მამუკაჯიბლაძე Yes, that identity follows from the Riemann addition relation of theta functions, see relation (5) in mathworld.wolfram.com/QuintupleProductIdentity.html | |
| Jul 14, 2017 at 18:58 | answer | added | Gjergji Zaimi | timeline score: 14 | |
| Jul 14, 2017 at 18:36 | comment | added | მამუკა ჯიბლაძე | Coefficients of lhs seem to be A206958 in OEIS. If so then according to that page, it is the expansion of$f(x^5,-x^7) -xf(-x,x^{11})$, where$$f(a,b)=1 +(a+b) +(ab)(a^2+b^2) +(ab)^3(a^3+b^3) +(ab)^6(a^4+b^4) + (ab)^{10}(a^5+b^5)+...$$is the Ramanujan theta function with the infinite product representation $(-a;ab)_\infty(-b;ab)_\infty(ab;ab)_\infty$ | |
| Jul 14, 2017 at 17:31 | comment | added | მამუკა ჯიბლაძე | @ZachTeitler It is the series for the expansion of $\prod_i(1-x^i)$ but with different signs. | |
| Jul 14, 2017 at 17:30 | comment | added | Zach Teitler | What is that left hand side? Is there a pattern to the signs? Or are you just claiming that the coefficients are all $\pm 1$ (or $0$)? | |
| S Jul 14, 2017 at 17:07 | history | suggested | MAN-MADE | CC BY-SA 3.0 |
MathJex used
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| Jul 14, 2017 at 16:55 | review | Suggested edits | |||
| S Jul 14, 2017 at 17:07 | |||||
| Jul 14, 2017 at 16:35 | history | asked | David S. Newman | CC BY-SA 3.0 |